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### Floating Bearing Shaft Length Design and Calculator

Floating Bearing Shaft Length Design and Calculator

The practical use of rolling element bearings requires consideration of their installation, as well as correct selection. Bearing installation considerations include the bearing combination, the mounting of the bearings, shaft length increase in length due to temperature changes, and the provision of lubrication.

A typical application of rolling element bearings is the support of a rotating shaft. If the operating temperature of the machine varies, the shaft length can grow relative to the casing or mounting arrangement. An idea of the magnitude of the axial shaft growth can be estimated by

Eq. 1
ΔL = Lo · α · ΔT

where

ΔL = change in length (m),
Lo = original length (m),
α = coefficient of linear thermal expansion (per °C), an
ΔT = temperature rise (°C).

For a gas turbine engine the difference in temperature between the casing and the shaft can be 50 °C. If the original length of the steel shaft was 1.0 m the growth of the shaft would be

ΔL = Lo · α · ΔT
ΔL = 1.0 x 11 x 10-6 x 50
ΔL = 5.5 x 10-4
ΔL = 0.55 mm

This is a considerable axial movement within a machine and must be allowed for if significant loadings and resultant stresses and possible contact between stationary and rotating components are to be avoided. A typical solution to this kind of situation is to allow for a limited axial movement on one bearing as shown in Figure 1 and 2.

Figure 1 Basic bearing mounting using two deep groove ball bearings for a rotating horizontal shaft for moderate radial and axial loading.

Here the right-hand bearing is a cylindrical roller bearing, and the axial location of the roller is not fixed and can move or float axially to the limited extents of the race to take up any axial movement or expansion of the shaft.

Figure 2 Basic bearing mounting using a deep groove and a cylindrical roller bearing for moderate radial loads at the “locating deep groove bearing” and high radial load capacity at the cylindrical roller bearing.

${}^{}$Source

Mechanical Design Engineering Handbook
Peter R. N. Childs
2014

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